If $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$, then $$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}$$ has the value

If $$\cot (A+B)=0$$, then $$\sin (A+2 B)$$ is equal to

$$\tan \mathrm{A}+2 \tan 2 \mathrm{~A}+4 \tan 4 \mathrm{~A}+8 \cot 8 \mathrm{~A}=$$

If $$a \sin \theta=b \cos \theta$$, where $$a, b \neq 0$$, then $$a\cos 2 \theta+b \sin 2 \theta=$$